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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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 Posted: Sun Sep 02, 2007 8:33 pm Post subject: One-Step Challenge |
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Here is a puzzle I came across that I discovered can be solved using only a single advanced step. However, it's not so easy to spot.
| Code: | +-------+-------+-------+
| . . . | . . 5 | . . . |
| . 7 . | 4 . 9 | . . 8 |
| . 3 . | . 2 . | . 9 . |
+-------+-------+-------+
| . 8 1 | 2 . . | 5 4 . |
| . . . | . . . | . . . |
| . 6 2 | . . 8 | 1 3 . |
+-------+-------+-------+
| . 9 . | . 6 . | . 7 . |
| 3 . . | 7 . 1 | . 2 . |
| . . . | 5 . . | . . . |
+-------+-------+-------+ |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Mon Sep 03, 2007 1:40 pm Post subject: |
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Nothing more advanced than naked pairs to this point, then 'the step', then nothing more advanced than hidden singles.
| Code: |
*--------------------------------------------------------------------*
| 48 12 9 | 1368 1378 5 | 23467 16 12346 |
| 12 7 6 | 4 13 9 | 23 5 8 |
| 458 3 45 | 168 2 67 | 467 9 146 |
|----------------------+----------------------+----------------------|
| 79 8 1 | 2 37 367 | 5 4 69 |
| 79 45 3 | 16 1457 467 | 2689 68 269 |
| 45 6 2 | 9 45 8 | 1 3 7 |
|----------------------+----------------------+----------------------|
| 12 9 458 | 38 6 234 | 348 7 1345 |
| 3 45 458 | 7 489 1 | 4689 2 4569 |
| 6 12 7 | 5 3489 234 | 3489 18 1349 |
*--------------------------------------------------------------------*
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon Sep 03, 2007 5:41 pm Post subject: |
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could it be you guys are referring to a rather long chain linking r2c1 and r9c2?
Not sure I could call this a W-wing but it certainly does the trick by eliminating 2 from r1c2 and r7c2. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Mon Sep 03, 2007 6:08 pm Post subject: |
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as a slightly differnt approach, one could start coloring the '12' cells in box one and arrive rather swiftly at r5c8=1 => r9c8=1 => r9c2=2 and so on.
| Code: |
*--------------------------------------------------------------------*
| 48 1g2r 9 | 1368 1378 5 | 23467 16g 12346 |
| 1r2g 7 6 | 4 13r 9 | 2r3 5 8 |
| 458 3 45 | 168 2 67 | 467 9 146 |
|---------------------+----------------------+----------------------|
| 79r 8 1 | 2 37r 367 | 5 4 6r9 |
| 79 45 3 | 16 1457 467 | 2689 68gr 269 |
| 45 6 2 | 9 45 8 | 1 3 7 |
|---------------------+----------------------+----------------------|
| 12 9 458 | 38 6 234 | 348 7 1345 |
| 3 45 458 | 7 489 1 | 4689 2 4569 |
| 6 12 7 | 5 3489 234 | 3489 18 1349 |
*-------------------------------------------------------------------* |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Sep 03, 2007 9:14 pm Post subject: |
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Yes, a long XY-Chain is the one advanced step. There are at least two of them. (There's one that eliminates <6>s in Boxes 3 and 6.)
Nataraj,
Your coloring is not conventional multi-digit coloring because it involves several weak links. Rather, it is color marking the XY Chain implications. (In other words, it is identical to XY Chaining: your coloring reveals the XY Chain with <6> pincers I mentioned above.)
Also, I believe you meant to write "R5C8=8" and to mark the <6> as "rg" in R5C8.
If one first applies the X-Wing on <1> in C28, then conventional Medusa (multi-digit) coloring results in a "Medusa Wrap" that reveals this same contradiction:
| Code: | +-----------------+-----------------+-----------------+
| 48 1g2r 9 | 368 378 5 | 23467 1r6g 2346 |
| 1r2g 7 6 | 4 1g3r 9 | 23 5 8 |
| 458 3 45 | 1r68 2 67 | 467 9 146 |
+-----------------+-----------------+-----------------+
| 79 8 1 | 2 37 367 | 5 4 69 |
| 79 45 3 |#1g6r 1457 467 | 2689 #6r8g 269 |
| 45 6 2 | 9 45 8 | 1 3 7 |
+-----------------+-----------------+-----------------+
| 12 9 458 | 38 6 234 | 348 7 1345 |
| 3 45 458 | 7 489 1 | 4689 2 4569 |
| 6 12 7 | 5 3489 234 | 3489 18 349 |
+-----------------+-----------------+-----------------+ |
With the extra <1>s out of R1, we are able to exploit the strong links and quickly find two "red" <6>s in R5. Thus, all of the "red" values are removed and all of the "green" values placed.
Note that this conventional method of coloring is not restricted to bivalue cells (as seen in R3C4 for instance). |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Mon Sep 03, 2007 9:16 pm Post subject: |
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I found a 9-cell xy-chain that solved the puzzle in one time
But like Asellus said, very hard to spot. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Sep 03, 2007 9:24 pm Post subject: |
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| Quote: | | Yes, a long XY-Chain is the one advanced step. |
What about the W-Wing on 16? That solved it for me. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Sep 03, 2007 9:48 pm Post subject: |
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| Marty wrote: | | What about the W-Wing on 16? That solved it for me. |
Nice catch. I didn't see it.
One way or another, that <6> in R5C8 is definitely toast! |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Mon Sep 03, 2007 10:22 pm Post subject: |
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This is the 9-cell xy-chain, eliminating <3> R2C5.
[37][79][96][68][81][12][21][12][23]
| Code: |
+------------+---------------+----------------+
| 48 12 9 | 1368 1378 5 | 23467 16 12346 |
|h12 7 6 | 4 1-3 9 |i23 5 8 |
| 458 3 45 | 168 2 67 | 467 9 146 |
+------------+---------------+----------------+
|b79 8 1 | 2 a37 367 | 5 4 c69 |
| 79 45 3 | 16 1457 467 | 2689 d68 269 |
| 45 6 2 | 9 45 8 | 1 3 7 |
+------------+---------------+----------------+
|g12 9 458 | 38 6 234 | 348 7 1345 |
| 3 45 458 | 7 489 1 | 4689 2 4569 |
| 6 f12 7 | 5 3489 234 | 3489 e18 1349 |
+------------+---------------+----------------+
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Tue Sep 04, 2007 12:32 am Post subject: |
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| Quote: | | What about the W-Wing on 16? That solved it for me. |
This is what I referred to. |
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